Approximation Properties of New Lupas-type Operators

In this book, I studied the approximation properties of a sequence of Lupas-type operators L_n (f;x) on the space C[0,¿). Then I define the sequence L ¿_n (f;x) which represented a generalization of the operators L_n (f;x) on the space C_¿ [0,¿). I applying the development of Bauer and Donner on Korovkin theorem, and define the m-th order moment T ¿_(n,m) (x), also, I proved the Voronoviskaja-type asymptotic formula for the operators L ¿_n.Finally, I define the sequence L ¿_(n,m) (f;x) on the space C_(¿,q) ([0,¿)×[0,¿)) which represented an extension of the operators L ¿_n on two dimensions (x,y) also applying the development of Bauer and Donner on Korovkin theorem, then proved the Voronoviskaja-type asymptotic formula for the operators L ¿_(n,m) (f;x,y). All above results lead us to show that the three operators L_n, L ¿_n and L ¿_(n,m) have the same order of approximation.